In recent years, with the rapid spread of radio equipment as typified by a mobile phone, a filter device for high frequency communication has been developed, which transmits only electric signals in a specific frequency band and is obtained by combining two or more resonators that are made of piezoelectric materials and use surface acoustic waves (SAW) or bulk acoustic waves (BAW). So far, a dielectric filter and a SAW filter have been mainly used. However, a filter composed of a piezoelectric thin-film resonator has recently attracted much attention because the piezoelectric thin-film resonator exhibits good performance particularly at high frequencies, and also can be formed as a small monolithic device.
In the piezoelectric thin-film resonator, the vibration that propagates in a direction perpendicular to an electrode surface is defined as a fundamental mode of vibration. In some cases, there may be another mode of vibration that propagates in a direction parallel to the electrode surface. Such a vibration that propagates in the direction parallel to the electrode surface is called “transverse mode spurious”, which is noise for the fundamental mode of vibration.
Patent Document 1 discloses a piezoelectric thin-film resonator in which a plurality of holes are provided in a portion of an upper electrode that is located opposite a lower electrode across at least a part of a piezoelectric thin film. The plurality of holes are irregularly arranged and have irregular sizes or shapes, so that the transverse mode spurious can be suppressed.
Patent Document 1: JP 2007-184816 A
However, the inventors found that in the piezoelectric thin-film resonator disclosed in Patent Document 1, it is difficult to provide an arrangement method of the holes or a pattern design to suppress the transverse mode spurious.